The ARMAX model (ARIMA model with eXogenous inputs) is a generalization of the ARMA model by incorporating exogenous variables.
Xt is an ARMAX(p, q) process, for which
\[
X_t = \mu + \sum_{i=1}^p \phi_i X_{t-i} + \sum_{i=1}^q \theta_j \epsilon_{t-j} + \psi' D_t + \epsilon_t,
\]
where Dt is an (m * 1) vector which contains all exogenous variables at time t (excluding the intercept term),
and its coefficients are represented by an m-dimensional vector ψ.